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-(ArcTanh[x/a]/a)

Integrate[1/(-a^2 + x^2), x] ==
-(ArcTanh[x/a]/a) 

             1
Integrate[--------, x] == 
            2    2
          -a  + x

          x
  ArcTanh[-]
          a
-(----------)
      a
Time to compute: < 0.01 second
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